Details

analyze509.0ms (13.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
25%	74.9%	0.2%	7
25%	74.9%	0.2%	8
34.3%	65.5%	0.2%	9
39%	60.8%	0.2%	10
48.3%	51.5%	0.2%	11
53.7%	46.1%	0.2%	12
63.1%	36.7%	0.2%	13
64%	35.6%	0.4%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample165.0ms (4.5%)

Algorithm

1×

intervals

Symmetry

(sort z t)

Results

12.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

100×	`fma-def_binary64`
56×	`fma-neg_binary64`
28×	`cancel-sign-sub-inv_binary64`
18×	`sub-neg_binary64`
13×	`distribute-rgt-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

2.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.0b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (*.f64 z t))
✓	2.0b	(/.f64 x (-.f64 y (*.f64 z t)))

series45.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

37.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
8.0ms	(-.f64 y (*.f64 z t))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 51

Calls

2 calls:

3.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
2.0ms	(-.f64 y (*.f64 z t))

simplify82.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

761×	`associate-/l*_binary64`
527×	`associate-/r*_binary64`
388×	`fma-def_binary64`
188×	`fma-neg_binary64`
173×	`associate-*l/_binary64`

Counts

135 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	2389
1	332	2275
2	1159	2114
3	4821	2114
4	4954	2114

prune80.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	8	111

Error

1.9b

Counts

111 → 8

Alt Table

Status	Error	Program
✓	2.0b	(/.f64 x (-.f64 y (*.f64 z t)))
	30.1b	(/.f64 x y)
	2.7b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
▶	2.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	2.5b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	2.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))
	33.5b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	3.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 y (.f64 z t)))))

Compiler

Compiled 1971 to 599 computations (69.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.1b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	2.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series60.0ms (1.6%)

Counts

2 → 84

Calls

2 calls:

40.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
20.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`associate-r_binary64`

Counts

2 → 75

Calls

2 calls:

7.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
3.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

simplify103.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-/r*_binary64`
540×	`fma-def_binary64`
347×	`associate-*l/_binary64`
222×	`fma-neg_binary64`
200×	`associate-/l/_binary64`

Counts

159 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	3528
1	394	3335
2	1569	3102
3	4897	3102
4	5060	3102

prune156.0ms (4.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	184	7	191

Error

1.9b

Counts

191 → 7

Alt Table

Status	Error	Program
	24.6b	(.f64 x (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (-.f64 y (.f64 z t)) (-.f64 y (.f64 z t))) (-.f64 y (.f64 z t))))))
	2.7b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	29.5b	(.f64 (.f64 x (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t))))) (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))
▶	2.5b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	2.0b	(/.f64 x (-.f64 y (*.f64 z t)))
	30.1b	(/.f64 x y)
	33.5b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))

Compiler

Compiled 3423 to 1364 computations (60.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.6b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	2.0b	(/.f64 (-.f64 y (*.f64 z t)) x)

series54.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

36.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
18.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 110

Calls

2 calls:

5.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
4.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

simplify128.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

794×	`associate-/l*_binary64`
526×	`associate-/r*_binary64`
409×	`fma-def_binary64`
329×	`associate-/r/_binary64`
251×	`associate-/l/_binary64`

Counts

206 → 188

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	4158
1	402	3845
2	1455	3696
3	4932	3696
4	5008	3696

prune147.0ms (4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	226	7	233

Error

1.9b

Counts

233 → 7

Alt Table

Status	Error	Program
	29.5b	(.f64 (.f64 x (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t))))) (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))
✓	2.5b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	2.0b	(/.f64 x (-.f64 y (*.f64 z t)))
	30.1b	(/.f64 x y)
▶	2.7b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	33.5b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	25.3b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (-.f64 y (*.f64 t z)) x) 3)))

Compiler

Compiled 4291 to 1370 computations (68.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.5b	(cbrt.f64 x)
✓	1.1b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
✓	1.2b	(/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x))

series355.0ms (9.7%)

Counts

4 → 120

Calls

4 calls:

234.0ms	(/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x))
47.0ms	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
40.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
33.0ms	(cbrt.f64 x)

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
62×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-cube-cbrt_binary64`
49×	`cbrt-prod_binary64`

Counts

4 → 165

Calls

4 calls:

8.0ms	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
4.0ms	(/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify204.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-def_binary64`
412×	`unswap-sqr_binary64`
344×	`associate-/l*_binary64`
220×	`div-sub_binary64`
183×	`times-frac_binary64`

Counts

285 → 293

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	254	5914
1	620	5095
2	2919	4957
3	4021	4873
4	4838	4873
5	4976	4873

prune168.0ms (4.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	328	1	329
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	329	7	336

Error

1.9b

Counts

336 → 7

Alt Table

Status	Error	Program
	29.5b	(.f64 (.f64 x (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t))))) (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))
✓	2.5b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	2.7b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	47.6b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 y (pow.f64 (/.f64 1 x) 1/3)))
✓	2.0b	(/.f64 x (-.f64 y (*.f64 z t)))
	33.5b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	25.3b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (-.f64 y (*.f64 t z)) x) 3)))

Compiler

Compiled 7210 to 1500 computations (79.2% saved)

regimes607.0ms (16.6%)

Accuracy

Total 0.1b remaining (2%)

Threshold costs 0.1b (2%)

Counts

92 → 1

Compiler

Compiled 11329 to 7341 computations (35.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	30	10
4	34	10
5	35	10
6	35	10

end5.0ms (0.1%)

Remove: (sort z t)
Compiler: Compiled 33 to 21 computations (36.4% saved)

sample675.0ms (18.4%)

Algorithm

1×

intervals

Results

288.0ms	8000×	body	128	valid
12.0ms	356×	body	128	invalid

Compiler

Compiled 140 to 92 computations (34.3% saved)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

Details

analyze509.0ms (13.9%)

sample165.0ms (4.5%)

simplify14.0ms (0.4%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series45.0ms (1.2%)

rewrite8.0ms (0.2%)

simplify82.0ms (2.2%)

prune80.0ms (2.2%)

localize6.0ms (0.2%)

series60.0ms (1.6%)

rewrite15.0ms (0.4%)

simplify103.0ms (2.8%)

prune156.0ms (4.3%)

localize6.0ms (0.2%)

series54.0ms (1.5%)

rewrite16.0ms (0.4%)

simplify128.0ms (3.5%)

prune147.0ms (4%)

localize9.0ms (0.2%)

series355.0ms (9.7%)

rewrite33.0ms (0.9%)

simplify204.0ms (5.6%)

prune168.0ms (4.6%)

regimes607.0ms (16.6%)

simplify5.0ms (0.1%)

end5.0ms (0.1%)

sample675.0ms (18.4%)

Profiling

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10